Queuing Theory 6t12e

Queuing Theory A mathematical method of analyzing the congestions and delays of waiting in line. Queuing theory examines every component of waiting in line to be served, including the arrival process, service process, number of servers, number of system places and the number of "customers. Real-life applications of queuing theory include providing faster customer service, improving traffic flow, shipping orders efficiently from a warehouse and deg telecommunications systems such as call centers.

Components Of Queuing Process

BASIC COMPONENTS OF A QUEUING SYSTEM INPUT SOURCE OF QUEUE An input source is characterized by • Size of the calling population • Pattern of arrivals at the system • Behaviour of the arrivals Size of the calling population— The size represents the total number of potential customers who will require service. According to source The source of customers can be finite or infinite. According to numbers The customers may arrive for service individually or in groups.

According to time Customers arrive in the system at a service facility according to some known schedule (for example one patient every 15 minutes or a candidate for interview every half hour) or else they arrive randomly. Pattern of arrivals at the system— The arrival process (or pattern) of customers to the service system is classified into two categories: static and dynamic. In static arrival process, the control depends on the nature of arrival rate (random or constant). Random arrivals are either at a constant rate or varying with time. Thus to analyze the queuing system, it is necessary to attempt to describe the probability distribution of arrivals. From such distributions we obtain average time between successive arrivals, also called inter-arrival time (time between two consecutive arrivals), and the average arrival rate (i.e. number of customers arriving per unit of time at the service system). The dynamic arrival process is controlled by both service facility and customers. The service facility adjusts its capacity to match changes in the demand intensity, by either varying the staffing levels at different timings of service, varying service charges (such as telephone call charges at different hours of the day or week) at different timings, or allowing entry with appointments. SERVICE SYSTEM The service is provided by a service facility There are two aspects of a service system—(a) the configuration of the service system and (b) the speed of the service. a) Configuration of the service system i Single Server – Single Queue -- The models that involve one queue – one service station facility are called single server models where customer waits till the service point is ready to take him for servicing. Students arriving at a library counter is an example of a single server facility.

i i S i n g l e S e r v e r – S e v e r a l Q u e u e s – I n t h i s t y p e o f fa c i l i t y there are s e v e r a l q u e u e s a n d t h e c u s t o me r may j o i n a n y o n e o f t h e s e but there is only one service channel.

iii Several (Parallel) Servers – Single Queue – In this typ e o f mo d e l t h e r e i s mor e t h a n o n e s e r v e r a n d e a c h s e r v e r p r o v i d e s t h e s a me t y p e o f fa c i l i t y . T h e c u s t o me r s w a i t i n a s i n g l e q u e u e u n t i l o n e o f the service channels is ready to take them in for servicing.

i v S e v e r a l S e r v e r s – S e v e r a l Q u e u e s – T h i s t y p e o f mo d e l c onsists of several servers where each of the servers has a different q ueue. Different c a s h c o u n t e r s i n a n e l e c t r i c i t y o f f i c e w h e r e t h e c u s t o me r s c a n mak e

p a y me n t i n r e s p e c t o f t h e i r e l e c t r i c i t y b i l l s p r o v i d e a n e x a mp l e o f t h i s t y p e o f mo d e l .

v S e r v i c e f a c i l i t i e s i n a s e r i e s – I n t h i s , a c u s t o me r e n t e r s t h e fir s t s t a t i o n a n d g e t s a p o r t i o n o f s e r v i c e a n d t h e n mo v e s o n t o the next s t a t i o n , g e t s s o me s e r v i c e a n d t h e n a g a i n mo v e s o n t o t h e n ext station. …. a n d s o o n , a n d f i n a l l y l e a v e s t h e s y s t e m, h a v i n g r e c e i v e d t h e c o mpl e t e s e r v i c e . F o r e x a mp l e , ma c h i n i n g o f a c e r t a i n s t e e l i t e m may consist of cutting, turning, knurling, drilling, grinding, and packagi ng operations, e a c h o f w h i c h i s p e r f o r med b y a s i n g l e s e r v e r i n a s e r i e s .

QUEUE CONF IGURAT ION The queuing process refers to the number of queues, and their respective lengths. The number of queues depend upon the layout of a service

system. Length (or size) of the queue depends upon the op erational situation such as • physical space, • legal restrictions, and • attitude of the customers. QUEUE DI SCI P L INE (a) Static queue disciplines are based on the individual cu stomer's status in the queue. i If the customers are served in the order of their arrival, then this is known as the first-come, first-served (FCFS) service disci pline i i L a s t - c o m e - f i r s t - s e r v e d ( L C F S )- - S o m e t i m e s , t h e c u s t o m e rs are serviced in the reverse order of their entry so that the one s who the last are served first. (b) Dynamic queue disciplines are based on the individual customer attributes in the queue. i S e r v i c e i n R a n d o m O r d e r ( S I R O )- - U n d e r t h i s r u l e c u s t o mers are selected for service at random, irrespective of their arriv als in the service system. In thisevery customer in the queue is equa lly likely to be selected. i i P r i o r i t y S e r v i c e- - U n d e r t h i s r u l e c u s t o m e r s a r e g r o u p e d in priority classes on the basis of some attributes such as service tim e or urgency or according to some identifiable characteristic, and FCFS ru le is used within each class to provide service

Network Management System A network management system (NMS) is a system comprising software and hardware that is responsible for the direct management of the communication and computing hardware and software in the network. NMSs are defined in a two ways: rules-based and policy-based. the rules-based systems have predominated. In such systems, a set of simple commands are sent to individual network elements (routers/switches) one at a time. Policy-based management allows active management of network resources based on s and applications. It requires a new set of protocols and a tighter correlation between the managed and managing devices. Network management covers a wide area, including:  Security: Ensuring that the network is protected from unauthorized s.  Performance: Eliminating bottlenecks in the network.  Reliability: Making sure the network is available to s and responding to hardware and software malfunctions.

Components of a Network Management System A NMS is limited by the capabilities of the network management protocol and the data objects used to represent the environment to be managed. A network management system contains four basic components. 

One or more managed nodes, each of which executes software that acts as an agent on its behalf. Although not called a server, the agent acts similarly. It provides information on request; it is the responder.

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At least one network management station (NMS) on which network management applications execute, often referred to as the manager. The network management station retrieves data from the agents, as required to perform the management functions. (Again, although not a client per se, the network management station acts similarly. It retrieves and uses the information from the agent, and may cause the agent to perform some action.

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A network management protocol, which is used by the station and agents to format and exchange management messages. Simple Network Management Protocol (SNMP) and Common Management Information Protocol (CMIP) are two examples. Although SNMP and CMIP are often used to refer to the entire management system, they actually define only this exchange protocol. More recentlyHTTP has been used to transport management information to a client Web-based interface.

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The management information, which is stored in the management information base (MIB). The storage device for this information may be a disk or memory.

The ISO network management model's five functional areas are listed below.

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Fault Management—Detect, isolate, notify, and correct faults encountered in the network. Configuration Management—Configuration aspects of network devices such as configuration file management, inventory management, and software management. Performance Management—Monitor and measure various aspects of performance so that overall performance can be maintained at an acceptable level. Security Management—Provide access to network devices and corporate resources to authorized individuals. ing Management—Usage information of network resources.